I am having a hard time putting the differentiation equation together maybe someone could point me the in right direction. here is the problem :


A particular factory manufactures n units per month. Each unit sells for c dollars. The number of units sold varies with the selling price according to

n=600-10c

and the monthly operating cost of the factory is given by
C=4000+12n

The monthly profit
P=nc-C

is the maximum when the unit selling price is
(1) $42
(2) $36
(3) $420
(4) $90

I am just having a hard time getting the equation for it. I guess I am stuck deep just need a kick start.

thanks for any help anyone could give me some advice.

 

Well, maybe the following will help you:

You want the maximum dependent variable profit P in terms of the independent variable unit price c.

Let me ask you. If you wanted to find the local max/min of a function y(x) how would you go about doing that?

Hope this helped. Good luck,

-blazed

 

Play arond with eqn until you can express P in terms of c only. You shld get a quadratic equation.

Thereafter find DP/Dc when it is 0. you shld get the answer.

 

thanks for your (the two of you) help. I was heading in the right direction. Just wasn't sure. it is hard to do problems with a flashlight in the dark. I know I made a couple of small mistakes.

 

The correct answer is $36 if that helps.